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Harmony of the World

Edited by Gerald Alexanderson with the assistance of Peter Ross

Who would expect to find in Mathematics Magazine an interview by Mike Wallace of 60 Minutes of a 12-year-old boy in New York who had published an article on a number system with an irrational base and who would go on to a significant career as a professor of mathematics at the University of California, Berkeley? And who would expect to find in the pages of the Magazine the first full treatment of one of the more important and oft-cited twentieth century theorems in analysis, the Stone-Weierstrass Theorem—in an article by Marshall Stone himself. Where else would one look for proofs of trigonometric identities using commutative ring theory? Or one of the earliest and best expository articles on the then new Jones knot polynomials, an article that won the prestigious Chauvenet Prize? Or an amusing article purporting to show that the value of pi has been time dependent over the years? This and much more is in this collection of the "best" from Mathematics Magazine.

Readers are inundated with new material in the many mathematical journals. Gems from past issues of Mathematics Magazine or the Monthly or the College Mathematics Journal are read with pleasure when they appear, but get pushed into the background when the next issues arrive. So from time to time it is rewarding to go back and see just what marvelous material has been published over the years, articles not to some extent forgotten. There is history of mathematics (algebraic, numbers, inequalities, probability, and the Lebesque integral, quaternions, Pólya's enumeration theorem, and group theory) and history of mathematicians (Hypatia, Gauss, E.T. Bell, Hamilton, and Euler).